Metallic radius listed

The atom radius of an element is the shortest distance between like atoms. It is the distance of the centers of the atoms from one another in metallic crystals and for these materials the atom radius is often called the metal radius. Except for the lanthanides (CN = 6), CN = 12 for the elements. The atom radii listed in Table 4.6 are taken mostly from A. Kelly and G. W. Groves, Crystallography and Crystal Defects, Addison-Wesley, Reading, Mass., 1970. 

A wide variety of techniques has been used to investigate the interaction between inorganic cations and polyelectrolytes in aqueous solution. The results are usually given in the form of a sequence of metal cations listed in order of increasing interaction with the polyelectrolyte. For the alkali metal cations the sequence of increasing interaction with carboxylated Q, and phosphated polyelectrolytes O) parallels the decrease in ionic radius. The sequence is reversed for the interaction with sulphated polyelectrolytes. (, ... 

Strictly speaking, the values of atomic radius listed above can only be used to describe the size of atoms in the metallic state of pure elements, because the real atomic radius of metallic state are rather flexible to change significantly due to charge transfer between different kinds of atoms in intermetallic compounds or alloy systems. But even so these values are still very useful atomic parameters if we use them together with the difference of electronegativities for the describing of the physico-chemical phenomena related to intermetallic compounds or alloy systems. 

The formability of intermetallic compounds can be investigated by SVM and the atomic parameters suitable for metallic systems, i.e., Midema s electronegativity (< )), metallic radius (R), number of valence electrons (Z) of free atom and parameter and their functions. For example. Table 6.3 lists the data about the formability of ternary intermetallic compounds and related atomic parameters of known Mg-containing ternary alloy systems. By support vector classification with Gaussian kernel, the rate of correctness of classification is 100%, and the rate of correctness of prediction in LOO cross-validation is 94.9%. 

It can be seen that the results of SVR computation are rather satisfactory. Moreover, it has been found by SVR computation that the inclusion of radius ratio of metallic atoms significantly improves the accuracy of enthalpy prediction. A reasonable explanation of this fact is that the rare earth-transition metal compounds listed here do not have the... 

The entropies of the metals heavier than americium have been estimated by Ward and his colleagues [22,32-37] from those of the lighter actinide metals by correlation with metallic radius, atomic weight, and magnetic entropy. These entropies have been accepted by David [25,27] and by Ward [38] and are also listed in Table 17.1. 

The number of solvent molecules to be packed around and next to an ion of radius r, as a first shell, increases with the size of the ion. For instance (and we should not worry at this stage about the details of the method, nor about the accuracy of these numbers), Fabricand used an NMR method in 1964 (17) to determine the hydration numbers n of the alkali metal cations, listed below with their ionic radii r (Table 6). Evidently, the hydration number n, i.e., the number of nearest neighbor (coordinating) solvent molecules goes up as r, in proportion to the size of the outer surface of the ion. Pauling was the first, in the 1930s, to draw attention to this factor. 

The uncertainty of the proper coordination number of any particular plutonium species in solution leads to a corresponding uncertainty in the correct cationic radius. Shannon has evaluated much of the available data and obtained sets of "effective ionic radii" for metal ions in different oxidation states and coordination numbers (6). Unfortunately, the data for plutonium is quite sparse. By using Shannon s radii for other actinides (e.g., Th(iv), U(Vl)) and for Ln(III) ions, the values listed in Table I have been obtained for plutonium. These radii are estimated to have an uncertainty of 0.02 X ... 

Binary and ternary structure types with isolated B atoms are listed in Table 1. In the metal borides of the formula (My, Mi ),B or T,(B, E) (M-p, M - = transition metals, E = nonmetal), the influence of the radius ratio as well as the... 

The remaining compounds listed in Table II all adopt structures with infinite metal-metal bonded chains consisting of octahedral cluster units fused on opposite edges. However, because of the large difference in effective ionic radius of the cations concerned, very different lattice types are dictated. The compounds NaMoi 06 (19,22) and Bas(Moit06)8 (17) adopt tunnel structures with the Na+ or Ba2+ ions located in sites along the tunnels with 8-fold coordination by oxygen atoms. 

However, since only values of rexpti are obtained, it is necessary to assume a value for the ionic radius of either r+ or r- in order to derive the ionic radius of the other. It is usual to assume a value of 1.40 A for the radius of the and 1.94 A for the radius of CP (Pauling, 1948) because these are half the minimum anion-anion distances found in crystal structures. Values for ionic radii (Shannon and Prewitt, 1969 Shannon, 1976 Brown, 1988) are listed in Table V for a coordination number of 6 around the metal atoms. Thus, values of radii are hypothetical, based on the idea of an additivity rule and a few initial assumptions on anion size. 

In 1967, C. J. Pederson of DuPont deNemours Co. synthesized the cyclic polyethers ( ) These cyclic polyethers are commonly referred to as "crown ethers" (see Figure 3). In solution, crown ethers are extremely effective ligands for a wide range of metal ions. The size of the ring cavity and the ionic radius of the metal affect the stability of the complex. Tables I and II list the cavity diameters for the crown ethers and the ionic radii of a number of metal ions (6-11). 

Many simple minerals, especially simple salts like halite, NaCl, sulfides, sulfosalts and oxides, have structures based upon cubic or hexagonal closest-packed arrays of either cations or anions. Coordination geometries of metal ions in many of these kinds of minerals are thus confined to more or less regular octahedra and tetrahedra. The occupancy of the two types of sites is dictated by the stoichiometry of the mineral, the radius of the ions involved and their preferred coordination geometries. Coordination of cations in mineral species in terms of bonding and crystal field effects has been extensively reviewed.16-21 Comprehensive lists of ionic radii relevant to cation coordination geometries in minerals have also been compiled.16,21... 

Both scandium and yttrium are electropositive metals with similar reduction potentials to the lanthanides ( °Sc +/Sc = -2.03 V ° Y +/Y = —2.37 V compare values of-2.37 V and -2.30 V for La and Lu, respectively). The ionic radii of Sc + and Y + are 0.745 A and 0.900 A, respectively (in six coordination). The former is much smaller than any Ln + ion but yttrium is very similar to Ho + (radius 0.901 A) purely on size grounds, it would be predicted that yttrium would resemble the later lanthanides but that scandium would exhibit considerable differences, and this expectation is largely borne out in practice. Table 7.1 lists stability constants for typical complexes of Sc + and Y +, together with values for La + andLu +. 

Knergy bands for the transition metals are constructed, using a minimal basis set of aiomic orbitals. The eleven parameters required are reduced to two, the d-band width H, and its position relative (o the. s-band minimum, using Muflin-Tin Orbital theory. Relations giving W, and all interatomic matrix elements in terms of a d-statc radius r,i and the intcrmicicar distance are listed in the Solid State Table, along with values of r, and E,t for all of the transition elements this makes possible elementary calculations of the bands for any transition metal, at any atomic volume. 

For analysis of the transition metals themselves, the use of free-electron bands and LCAO d states is preferable. The analysis based upon transition-metal pseudopotential theory has shown that the interatomic matrix elements between d states, the hybridization between the free-electron and d bands, and the resulting effective mass for the free-electron bands can all be written in terms of the d-state radius r, and values for have been listed in the Solid State Table. 

H H distances coupled with shorter M H distances. However, one has to account for differences in metallic radii, and so in column (iv) the adjusted M-H distances are hsted in which the differences in atomic radii are used as correction factors , with the atomic radius of iron selected arbitrarily as a standard . One can see that colunm (iv) is somewhat smoother than column (iii). Finally, recognizing that one should perhaps consider metal-ligand distances instead of metal-hydrogen distances, two extra columns have been included in which M-X distances are tabulated, where X is the midpoint of the H-H bond. Once again, the unadjusted and adjusted values [columns (v) and (vi) respectively] are listed, in which column (vi) contains the values corrected for differences in atomic radii. 

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